find the length and breadth of the rectangle

Question

The length of a rectangle exceeds its breadth by 7 cm. If the length is decreased by 4 cm and the breadth is increased by 3. The area of the new rectangle is the same as the area of the original rectangle. Find the length and breadth of the original rectangle 

Answer 1

You probably asked this question because the terminology "breadth" confused you.  This means width of rectangle.  Why couldn't the textbook use a simple term such as "width", which everyone knows well?  Don't ask me.  Ask the complicated developers of the textbook.  Well anyway, here is how you solve the problem.

 

First define variables for the rectangle's dimensions.

 

Dimensions of the original rectangle:

 

Let width = x

Let length = x + 7

 

 

Dimensions of new rectangle:

 

width = x + 3

length = (x + 7) - 4 = x + 3

 

 

Now using these variables, we create equations to represent the areas of the rectangle accordingly.  You know the area of rectangle is length times width.

 

Equate the original area to the new area.

 

x(x + 7) = (x + 3)(x + 3)

 

 

Solve this equation for x.

 

x² + 7x = x² + 6x + 9

 

 

Subtracting x² on both sides,

 

7x = 6x + 9

 

 

Subtracting 6x on both sides,

 

x = 9

 

 

Then all you have to do is substitute this value of x into the original dimensions.

Answer 2

w=w

l=w+7

 

(w+7)-4

(w+3)

 

[(w+7)-4][w+3]=(w)(w+7)

(w+3)(w+3)=(w)(w+7)

w^2+6w+9=w^2+7w

6w+9=7w

9=7w-6w

9 cm=width

9+7=16 cm

16 cm=length